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Fixed-time Input-to-state Stability via Generalized Homogeneous Approximations

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  • Control Theory and Applications
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Abstract

In order to extend the existing fixed-time control robustness results for double-integrator systems to general nonlinear systems, the fixed-time input-to-state stability (FT-ISS) of a class of nonlinear system with bounded exogenous disturbances is studied through generalized homogeneous approximations in this paper. To this end, the definitions of finite-time and fixed-time class \({\cal K}{\cal L}\) functions are given. Based on the definitions, the sufficient conditions of the FT-ISS property with respect to exogenous disturbances are proposed. Then, a class of fixed-time filters is designed under the principle of generalized homogeneous approximations. As a particular example, the stability and frequency characteristics of the low-pass fixed-time filter are analyzed by the presented sufficient conditions and describing function method, respectively. Finally, a simulation example is presented to illustrate the efficiency of the fixed-time filter.

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Authors and Affiliations

  1. School of Mechanical Engineering, Zhejiang University, 38 Zheda Rd., Hangzhou, 310027, China

    Libin Wang

  2. AVIC **’an Aircraft Industry (Group) Company Ltd., 1 **fei Rd., **’an, 710089, China

    Changxi Deng

  3. School of Information Science and Engineering, NingboTech University, 1 South Qianhu Rd., Ningbo, 315100, China

    Zemin Pan

  4. State Key Lab of Fluid Power Transmission and Control, Zhejiang University, 38 Zheda Rd., Hangzhou, 310027, China

    Qiang Fang

Authors
  1. Libin Wang
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Correspondence to Zemin Pan.

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The authors ensure that there is no potential conflict of interest possibly influencing the interpretation of data in the paper. The authors declare that there is no competing financial interest or personal relationship that could have appeared to influence the work reported in this paper.

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This work was supported by the China Postdoctoral Science Foundation (Grant No. 2021M692784), the National Natural Science Foundation of China (Grant No. 52005436, 51975519), and the Zhejiang Provincial Program for High-Level Talents(Grant No. 2021R52038).

Libin Wang received his B.S. degree in control science and engineering from Hebei University of Technology in 2012, his M.S. and Ph.D. degrees in control science and engineering from Harbin Institute of Technology (HIT) in 2014 and 2020. From 2016 to 2018, he was a visiting Ph.D. student in Mechanical and Aerospace Engineering, University of California, San Diego, CA, US. He is currently with the School of Mechanical Engineering, Zhejiang University, Hangzhou, China. His research interests include extremum seeking, adaptive control, and intelligent test method of aircraft airborne system.

Changxi Deng received his B.S. degree in mechanical design and manufacturing from Jiamusi University, Jiamusi, China, in 2006 and an M.S. degree in mechanical engineering from Zhejiang University, Hangzhou, China, in 2015. He is a Professorate Senior Engineer with AVIC **’an Aircraft Industry Group Company LTD. He is mainly engaged in the application research of intelligent control technology in the field of aviation manufacturing.

Zemin Pan was born in Ningbo, China, in 1987. He received his B.S. and Ph.D. degrees from the Department of Mechanical Manufacture and Automation, Zhejiang University, Hangzhou, China, in 2016. He has been working at NingboTech University since 2016 and is currently an Associate Professor. His research interests include aircraft digital assembly system and control technique, motion control and adaptive control of electromechanical systems.

Qiang Fang was born in Shaoxing, China, in 1975. He received his B.S., M.S., and Ph.D. degrees from Harbin Institute of Technology, Harbin, China, in 2006. He worked as a Postdoctoral Researcher at Zhejiang University, Hangzhou, China, in 2006, where he is currently a Professor. His research interests include aircraft digital assembly system and control technique, motion control, and robust control. He has published more than 30 papers in the International Journal of Modeling, Identification and Control, Chinese Journal of Mechanical Engineering, and Journal of Zhenjiang University (Engineering Science), etc.

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Wang, L., Deng, C., Pan, Z. et al. Fixed-time Input-to-state Stability via Generalized Homogeneous Approximations. Int. J. Control Autom. Syst. 22, 116–126 (2024). https://doi.org/10.1007/s12555-022-0719-y

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  • DOI: https://doi.org/10.1007/s12555-022-0719-y

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